Graphing Absolute Value Functions
F.IF.7 Graph functions expressed symbolically and show key features of the graph...Also F.IF.4, F.BF.3
Student Goals
Students will be able to identify and graph absolute value functions.
Absolute Value Functions
An absolute value function has a V-shaped graph that can open up or down. There is a parent function that is y=|x|. In other words, y equals the absolute value of x.
Translation
A translation is when you can move the graph horizontally (side-to-side), vertical (up or down), or both. The result of this process is to show that you can have the same graph, but in a different position. If we have some positive number called k, it will translate the graph y=|x|+k up k units. Meanwhile, if we have some k that is negative, y=|x|-k, the graph will move downwards k units.
Think of this as just moving the graph, but not exactly changing it. Though, we can do that too, but more for later.
The first function in the graph is the parent function. The functions under it are translations. There are all moved in some form or way. The general function for translations is y = |x-h| + k. Like above, the h will control how the function moves left and right, and the k will control how the function moves up and down. Play around with the function!
Try guessing how these functions are translated.
y = |x-4|
y = |x| + 2
y = |x+3|
External Resource
Graphs of absolute value functions